Question

class | female | male | total
1st | 133 | 59 | 192
2nd | 94 | 25 | 119
3rd | 79 | 59 | 138
total | 306 | 143 | 449

a) what is the probability that a survivor was female?
round final answer to 3 decimal places.

b) what is the probability that a survivor was in the 2nd class?
round final answer to 3 decimal places.

c) what is the probability that a survivor was a female given that the person was in 2nd class?
round final answer to 3 decimal places.

d) what is the probability that a survivor was a female and in the 2nd class?
round final answer to 3 decimal places.

e) what is the probability that a survivor was a female or in the 2nd class?
round final answer to 3 decimal places.

Explanation:

Part (a)

Step1: Identify total survivors and female survivors.

Total survivors (from "Total" row, "Total" column) is \( n = 449 \). Number of female survivors (from "Total" row, "Female" column) is \( f = 306 \).

Step2: Calculate probability.

Probability \( P(\text{female})=\frac{\text{Number of female survivors}}{\text{Total number of survivors}}=\frac{306}{449} \approx 0.6815 \), rounded to 3 decimal places is \( 0.682 \).

Step1: Identify total survivors and 2nd class survivors.

Total survivors \( n = 449 \). Number of 2nd class survivors (from "2nd" row, "Total" column) is \( c_2 = 119 \).

Step2: Calculate probability.

Probability \( P(\text{2nd class})=\frac{\text{Number of 2nd class survivors}}{\text{Total number of survivors}}=\frac{119}{449} \approx 0.2650 \), rounded to 3 decimal places is \( 0.265 \).

Step1: Identify 2nd class survivors and female 2nd class survivors.

Number of 2nd class survivors \( n_{2nd}=119 \). Number of female 2nd class survivors (from "2nd" row, "Female" column) is \( f_{2nd}=94 \).

Step2: Calculate conditional probability.

Conditional probability \( P(\text{female}|\text{2nd class})=\frac{\text{Number of female 2nd class survivors}}{\text{Number of 2nd class survivors}}=\frac{94}{119} \approx 0.7899 \), rounded to 3 decimal places is \( 0.790 \).

Answer:

\( 0.682 \)

Part (b)